1. Field of the Invention
This invention relates to a signal processing technique, and also to a computer program and a computer system for implementing the technique.
2. Discussion of Prior Art
A common requirement in signal processing is to monitor signals from a dynamic system such as a machine and to carry out procedures such as anomaly detection, condition monitoring, fault detection, signal-to-noise enhancement, background suppression and blind signal separation. The last is also known as independent component analysis, and the expression “blind” indicates that signal separation is carried out without knowledge of or assumptions concerning signal properties. It produces what are known as “separated signal components” which correspond to characteristic features of a signal being monitored.
Many prior art procedures require either prior knowledge of the characteristics of the system to be monitored, or alternatively labelling, classification or previous analysis of training data. An example of this is supervised “back-propagation” training for multi-layer perceptrons disclosed by Rumelhart D E, Hinton G E & Williams R J. in “Learning Internal Representations By Error Propagation”, which appears in Rumelhart & McClelland, Parallel Distributed Processing 1, MIT, 1986.
One known prior art technique in this area is referred to as “principal component analysis” or PCA: it may be defined as the process of determining eigenvectors of a covariance matrix of input data vectors, the matrix being obtained from subtracting the outer product of the mean data vector with itself from the mean outer product of each data vector with itself, in the conventional manner of statistics textbooks. The eigenvectors are a special case of parameters characterising a system and defined as “basis vectors” in standard texts on linear algebra. However, PCA is a linear technique and therefore cannot be used to extract features beyond a second order moment, i.e. higher-order features, or higher-order statistics. Many dynamical systems of interest in signal processing have higher-order statistics which cannot be extracted effectively by PCA. Similar remarks apply to linear neural networks such as linear perceptrons.
Rumelhart et al (ibid) and Minsky M L & Papert S A. Perceptrons, MIT, 1969 disclose non-linear perceptrons which it is known may be used to extract higher-order features. Moreover, this is an example of a neural network which implements a non-linear transformation of signals being processed. However, such techniques generally require prior knowledge, supervision, or manual labelling or classification of the training data, and even then do not necessarily extract practically useful or informative features. In this last regard convergence may occur at a false minimum remote from the solution that is useful in practice.
U.S. Pat. Nos. 5,377,306 and 5,453,940 are related patents disclosing an heuristic processor which is trained to fit training data to corresponding results empirically and then to use the form of the fit to predict hitherto unknown results using test data. Each describes deriving radial basis functions, these being functions of radial distances of input data from each of a set of origin points or centres: in a training mode the vectors are fitted to corresponding results by triangularisation of a matrix of these vectors; triangularisation is by a QR decomposition procedure used for solving an overdetermined set of linear equations and producing a least squares fit result. This determines a weight vector which when applied to a radial basis function provides an estimate of a corresponding result, which in turn can be compared with an actual result if available. Because the approach is non-linear it is suitable for extracting higher-order statistics; it provides signal reconstruction on the basis of training data and can be used for anomaly detection. However it suffers from the disadvantage that it is sensitive to the degree of time synchronisation of input signals, and also that only under certain circumstances does it extract useful features of the data.